IGCSEMathsCambridge (CIE)International MathsExtendedExam QuestionsLengths, Areas & VolumesCongruence & Similarity

Congruence & Similarity (Cambridge (CIE) IGCSE International Maths: Extended): Exam Questions

Exam code: 0607

3 hours46 questions

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Congruence & Similarity

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1
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2 marks
cie-igcse-2018-may-jun-3-p2-q25a

In the diagram, P Q is parallel to B C.
A P B and A Q C are straight lines.
P Q = 8 cm, B C = 10 cm and A B = 9cm.

Calculate P B.

P B = .......................................... cm

How did you do?

2a
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2 marks
screenshot-2023-05-26-at-4-26-02-pm

Quadrilaterals ABCD and LMNP are mathematically similar.

Angle A = angle L
Angle B = angle M
Angle C = angle N
Angle D = angle P

Work out the length of LP.

How did you do?

2b
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2 marks

Work out the length of BC.

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3
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3 marks
q4-medium-4-8-congurence-similarity-and-geometry-edexcel-gcse-maths

A B C and A E D are straight lines. B E and C D are parallel.
B E space equals space 1.5 space cm. space C D space equals space 6 space cm. space A D space equals space 5 space cm.

Calculate the length of E D.

How did you do?

4
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2 marks
cie-igcse-2018-oct-nov-p4-tz3-q8a

In the diagram, AB and CD are parallel.
AD and BC intersect at right angles at the point X.
AB = 10 cm, CD = 5 cm, AX = 8 cm and BX = 6 cm.

Use similar triangles to calculate DX.

 

 

DX = ........................................... cm

How did you do?

5
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3 marks

A solid cylinder with radius 1.6 cm is attached to the hemisphere to make a toy.

cie-igcse-2018-may-jun-1-6b

The total volume of the toy is 300 cm3.

A mathematically similar toy has volume 19 200 cm3.

Calculate the radius of the cylinder for this toy.

.......................................... cm

How did you do?

6
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2 marks
cie-igcse-2018-may-jun-3-p2-q25a

In the diagram, P Q is parallel to B C.
A P B and A Q C are straight lines.
P Q = 8 cm, B C = 10 cm and A B = 9cm.

Calculate P B.

P B = .......................................... cm

How did you do?

7a
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2 marks
screenshot-2023-05-26-at-4-26-02-pm

Quadrilaterals ABCD and LMNP are mathematically similar.

Angle A = angle L
Angle B = angle M
Angle C = angle N
Angle D = angle P

Work out the length of LP.

How did you do?

7b
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2 marks

Work out the length of BC.

How did you do?

8
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3 marks
q4-medium-4-8-congurence-similarity-and-geometry-edexcel-gcse-maths

A B C and A E D are straight lines. B E and C D are parallel.
B E space equals space 1.5 space cm. space C D space equals space 6 space cm. space A D space equals space 5 space cm.

Calculate the length of E D.

How did you do?

9
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2 marks
cie-igcse-2018-oct-nov-p4-tz3-q8a

In the diagram, AB and CD are parallel.
AD and BC intersect at right angles at the point X.
AB = 10 cm, CD = 5 cm, AX = 8 cm and BX = 6 cm.

Use similar triangles to calculate DX.

 

 

DX = ........................................... cm

How did you do?

10
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3 marks

A solid cylinder with radius 1.6 cm is attached to the hemisphere to make a toy.

cie-igcse-2018-may-jun-1-6b

The total volume of the toy is 300 cm3.

A mathematically similar toy has volume 19 200 cm3.

Calculate the radius of the cylinder for this toy.

.......................................... cm

How did you do?

1
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3 marks
q25-paper2-spec2025-cie-igcse-further-maths

The two shapes are mathematically similar.
The area of the larger shape is 36 cm2 and the area of the smaller shape is 25 cm2.
The height of the larger shape is 9 cm and the height of the smaller shape is x spacecm.

Find the value of x.

x space equals space................

How did you do?

2
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2 marks
cie-igcse-2018-may-jun-2-p2-q11

The diagram shows two mathematically similar triangles, T and U.
Two corresponding side lengths are 3 cm and 12 cm. The area of triangle T is 5 cm2.

Find the area of triangle U.

......................................... cm2

How did you do?

3
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3 marks

Rectangle A B C D is mathematically similar to rectangle D A E F.

q4-hard-4-8-congurence-similarity-and-geometry-edexcel-gcse-maths

A B space equals space 10 space cm. space A D space equals space 4 space cm.

Work out the area of rectangle D A E F.

How did you do?

4
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3 marks
q25-paper2-spec2025-cie-igcse-further-maths

The two shapes are mathematically similar.
The area of the larger shape is 36 cm2 and the area of the smaller shape is 25 cm2.
The height of the larger shape is 9 cm and the height of the smaller shape is x spacecm.

Find the value of x.

x space equals space................

How did you do?

5
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2 marks
cie-igcse-2018-may-jun-2-p2-q11

The diagram shows two mathematically similar triangles, T and U.
Two corresponding side lengths are 3 cm and 12 cm. The area of triangle T is 5 cm2.

Find the area of triangle U.

......................................... cm2

How did you do?

6
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3 marks

Rectangle A B C D is mathematically similar to rectangle D A E F.

q4-hard-4-8-congurence-similarity-and-geometry-edexcel-gcse-maths

A B space equals space 10 space cm. space A D space equals space 4 space cm.

Work out the area of rectangle D A E F.

How did you do?

1a
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3 marks
cie-igcse-2020-oct-nov-p4-tz2-q8c

 The diagonals of the cyclic quadrilateral ABCD intersect at X.  

Explain why triangle ADX is similar to triangle BCX. Give a reason for each statement you make.

How did you do?

1b
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2 marks

AD  = 10 cm, BC  = 8 cm, BX  = 5 cm, CX  = 7 cm.  

Calculate DX.

 

DX = ........................................... cm

How did you do?

2
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5 marks

The two triangles in the diagram are similar.

q4-veryhard-4-8-congurence-similarity-and-geometry-edexcel-gcse-maths

There are two possible values of x.

Work out each of these values.
State any assumptions you make in your working.

How did you do?

3
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5 marks

The diagram below shows two right-angled triangles.

q12-paper6-june2018-ocr-gcse-maths

Prove that triangles PQS and QRS are similar.

How did you do?

4
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5 marks

The two triangles in the diagram are similar.

q4-veryhard-4-8-congurence-similarity-and-geometry-edexcel-gcse-maths

There are two possible values of x.

Work out each of these values.
State any assumptions you make in your working.

How did you do?

5
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5 marks

The diagram below shows two right-angled triangles.

q12-paper6-june2018-ocr-gcse-maths

Prove that triangles PQS and QRS are similar.

How did you do?